When trying to play an old game, Skyroads for instance, I get the following error message:

The version of this file is not
compatible with the version of Windows
you're running. Check your computer's
system information to see whether you
need a x86 (32-bit) or x64 (64-bit)
version of the program, and then
contact the software publisher.

If I understand it correctly, Skyroads is a 16-bit program which is not supported in a 64-bit operating system? Is it impossible to get it running on a 64-bit operating system?

The short answer is no, it is not possible to run 16-bit application natively under Windows x64. The long answer is yes. If you're willing to try something like XPMode or other Virtualization software -- you can get it to work.

You can probably install this in xp mode of windows 7. You can download and install xp mode from microsoft. It will function similar to a virtual machine. I think this works in Windows 7 pro and above but there may be some hackery you can perform to get to function in win 7 Home.